Allocative efficiency and marginal benefit Microeconomics Khan Academy

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” ve already spent a nlot of time thinking about these six different nscenarios. All of of which sit on the production npossibilities frontier. Which means that in any nof. These we have achieved nproductive efficiency.

And it s true not just nof these scenarios. It s true of any of the npoints on this curve. So you have achieved nany point on that curve productive. Let nme give ourselves some real estate on nthe right efficiency.

Which means another nway to think about it is that as soon as you re nat. Any point on that curve if you want any more nof. One of these things you have to give up nsome of the other so for example. If nyou re at point c.

And if you want more rabbits nif. You want 1 more rabbit. You re going to have to ngive up some berries or if you re at point c. Nand.

You want more berries you re going to have to ngive up some rabbits and that s true of any point non the production possibilities frontier. A point over here let me ndo this in a different color. So let s say at this npoint. Right over here you have not achieved nproductive efficiency.

Here. Because you can get more nrabbits. Without having to give up any berries and you could get to scenario. Nb or you could get more berries and not have to ngive up any rabbits and you would get to scenario d.

So this right over nhere is inefficient. Now all of these nthat s all good all of these five nor six scenarios. We ve achieved nproductive efficiency. But which of these do we pick how do we decide to nallocate our time so what i want to talk nabout in this video is allocative efficiency.

And it s somewhat subjective nbased on the preferences of if we are the hunter gatherer nbased on our preferences. But at least it ngives us a framework for thinking. Which of these nmeets our preferences. The best and to do that i will review a nlittle bit from the last video in the last video.

We talked nabout the marginal cost of each incremental rabbit or. We said the opportunity cost nof each. Incremental rabbit and the opportunity cost of none incremental unit that really is just nthe marginal cost. So let s just write.

These ndifferent scenarios. So let s write. The scenarios. Nscenario for short scene.

For short. And then let s think nabout. The marginal cost of 1 incremental rabbit. I ll just draw a rabbit here and it s going to nbe given in berries.

All right let s start with nscenario f. And this is all review from nthe last video sitting in scenario f. If we nwant to get 1 extra rabbit. We are going to have nto give up 20 berries in scenario.

E. If we re nsitting in scenario. E. And we want even.

1. Nmore. Rabbit. We now have to give up 40 berries.

So the marginal cost at nthat point of 1. More i keep wanting to say squirrel. N1. More rabbit is 40 berries.

Now. Let s go to scenario..

D. Nand. I encourage you to pause. And do this yourself.

It ll help if you nkind of work. It out scenario d. The cost of 1 nextra. Rabbit.

Is now 60 berries. You go to scenario. C. The ncost is now 80.

Berries. So in scenario. C. The ncost is now 80.

Berries. Finally you got to nscenario b. And the cost of sitting in scenario b of ngetting 1 extra rabbit. You re going to have to ngive up.

100 berries. And i won t even ngo into scenario a because it will be impossible nfor you to have any more rabbits and you have no nmore berries to give up so these are all the npossible scenarios and the marginal costs of them. And we can actually nplot them on a line. So let me do that nright over here.

This will be useful. So. Let me draw. One axis right nover here one axis over here.

And this is let s call this nthe different scenarios. So this let me do nin. The same order. Let s call.

This nscenario f. Scenario. E. I.

ll just. Do. It. In.

None. Color. Right. Now.

Scenario. E. Scenario. D.

Scenario. Nc. And scenario. B.

Actually. Let. Me. Instead of ndoing.

It that way let me just talk nabout it in terms of the number of nsquirrels. I have so the number of nsquirrels that i have so in scenario f. If you nremember. In scenario f oh.

Not squirrels rabbits in scenario f you nhave 0 rabbits scenario f. You have 0 rabbits so let s say 0 n1 2 3 4 and 5 and so this is the number nof rabbits not squirrels the number of rabbits nthat..

You right now are able to catch non average each day and then in the vertical naxis right now i want to put the nmarginal cost in berries and let s see it goes. Nfrom. 20. Up to 100.

So. Let s say that this is n20 40. 60. 80 and 100.

So scenario f. That s nwhen. We had 0. Rabbits and the marginal cost of ntrying to get another rabbit.

You would have to ngive up. 20 berries. So that is scenario nf right over there scenario. E.

That s one where nwe had 1. Where we already had 1 rabbit. And we are nthinking about the marginal cost of getting another. One.

So. That s scenario. E. Nis.

Right over. There. This is scenario. D.

Nmarginal. Cost is 60. We already have 2. Nrabbits and we are thinking about getting a third that s scenario d.

And then scenario c. We nalready have 3. Rabbits thinking about getting a fourth that s scenario c. Nand.

Then finally we have scenario b. Where we nalready have 4 rabbits and we re thinking nabout. Getting a fifth and we would have to ngive up 100 berries to get that fifth rabbit. So that s scenario nb right over there so what i ve just done is nplotted the marginal cost along these are points on nessentially our marginal cost curve our marginal ncost as a function of the number of nrabbits.

We have so let me connect all the dots and then this scenario njust happened to be a line doesn t always have to be a nline. But in many introductory economics courses. It s noften. A line for simplicity.

So let me make this a nline right over here. This is our marginal ncost as a function of the number of nrabbits. We have and actually i should nprobably draw this axis. I should probably draw nlet me copy and paste this so let me cut this let me cut that and then let nme paste.

It because it really should sit on the 0 npoint. Right over there and ignore that little nline right over there so there you have marginal ncost as a function of berries. But we still don t know nwhich scenario to pick and to think about that i nwant to introduce something called the marginal benefit and i ll write it as nmb. The marginal benefit of an incremental rabbit and once again we re going nto write it in berries and the way to think nabout.

The marginal benefit is if we are the nhunter gatherer. We re saying if we re sitting in one of nthese scenarios. How much would we paid to some hypothetical nconvenience store. In berries.

Maybe that convenience nstore. Only sells bunnies and they only accept nberries. How much would we pay to them in berries nfor. An extra rabbit and let s not even look at nthis thing right over here.

So if we re sitting in scenario nf. We re sitting in scenario f..

And you remember scenario. Nf is right over here. We have no rabbits. How much would we nbe willing to pay we have no rabbits and we nactually have a ton of berries.

So in scenario f right nhere. We have no rabbits and we have 300 berries. If we have no rabbits nand. A lot of berries.

Let s say we ll say we nhave a lot of berries. We might be in the nmood for a rabbit. We would be willing to pay a nlot in berries for a rabbit. So let s say we would pay 100 we would pay 100 berries to nthat hypothetical convenience store for a rabbit now let s say that we re in nscenario e.

We re in scenario e. How much would we pay to that nhypothetical. Convenience store. Well in scenario e.

We nalready have 1 rabbit. And we have fewer berries. So we need a rabbit. Less and nwe have fewer berries to give so we re not willing to ngive.

Quite as many berries for another rabbit. So maybe we ll only ngive. 80. Berries.

Then you go to scenario d. We already have 2 rabbits and nwe have even fewer berries. So we re willing to ngive even fewer berries for another rabbit. This is what we would pay nto a convenience store just based on thinking about nit our current preferences.

Then we can go all nthe way to scenario c. And it is subjective. It s not like a nmeasurable thing. It s just based on this nperson s preferences this hunter gatherer s npreferences scenario c.

Well they already nhave more rabbits even fewer berries so they ll pay even less and then finally nscenario b. They have a good number of rabbits nand. Even fewer berries. They would be willing nto pay.

Very little for an incremental rabbit. So let s plot. The nmarginal benefit as a function of the number of nrabbits that they already have so if we go to scenario nf. The marginal benefit.

Doing that little thought nexperiment is 100 in scenario. E. The nmarginal benefit. How much you would nhypothetically be willing to pay in nberries.

Is now 80 berries in scenario. D. It is 60 berries in scenario. C.

It. Is 40. Berries. So scenario.

C. Is nright over here. So in scenario. C.

Nit s 40. Berries and then in scenario nb. It is 20 berries. So in scenario b.

It is 20 nvarious. Just like that so now we re not just nplotting..

The marginal cost. We re plotting the marginal ncost and the marginal benefit in berries and the marginal nbenefit curve. And it s really a line here. Once nagain for simplicity looks like that now given this.

So. This is nthe marginal benefit curve marginal benefit is a function nof. The number of rabbits that we already have and this is the marginal ncost as a function of the number of nrabbits. We already have and so when i say ne.

This is actually situation e. That s situation nd. This is also situation c. And this is also this is the nmarginal benefit at situation b.

So given this what nwould i rationally do if these really nare my preferences. What would i rationally do so if i m sitting here in nsituation f. I have no rabbits. I already know that it nwould cost me 20 rabbits to try to get an nincremental one.

But i ve already said that ni d be willing to pay 100 sorry it would ncost me 20 berries to get an incremental rabbit. But i ve already said nthat. I m willing to pay 100 berries to get an nincremental rabbit. So i would want to nmove along the curve so i would definitely nwant to get more rabbits.

I said that i m willing to npay 100 berries for a rabbit and it would only cost me n20 berries for a rabbit. So i m saying that i nwant to get more rabbits and another way to look at nthis visually marginal benefit is much higher than nmarginal cost here so i m willing to go forth nand try to get more rabbits that s even true in scenario ne. The marginal benefit of an incremental rabbit nis worth much more to me than the marginal cost nso. I m willing to try to get more rabbits so in scenario e.

I m still ntrying to get more rabbits. I still want to move along nthe production. Possibilities frontier in this ngeneral direction. Now what happens as ni get closer to d.

So if i m in this nscenario right over here and this isn t one of nour labeled scenarios. But if i m right nover. There still my marginal cost is lower nthan my marginal benefit. So i ll still want to get nmore rabbits.

All the way. Until i m scenario d in scenario d. I m a nlittle bit neutral. I m willing to pay 60 nberries for a rabbit.

But that s exactly nhow much. I d have to give up to get nthat extra rabbit. So let s just think about nscenario d. For a little bit.

I ll just circle nit right over here. Because it looks nkind of interesting now let s go nnow would we want to do anything nbeyond scenario d. So if i m at this npoint right over here if i m working nenough on average to say get. 2.

And n1 2 rabbits. A day would i does this nmake sense for me to try to get any more rabbits well at that point nthe benefit of getting an incremental rabbit nis. Smaller than the cost of getting a rabbit at that point. If i try nto get another rabbit.

I m getting less benefit from nit than the cost associated with it so i definitely don t nwant to move past d. So i achieve nallocative efficiency. Where my marginal cost and nmy marginal benefit is equal. So based on the way nthat.

I ve rigged the numbers in this nexample. Right over. Here. You want to settle.

Non scenario. D. We have achieved allocated nefficiency over there the marginal cost as a nfunction of our rabbits. ” .


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